We introduces the Binary Morphological Neural Network (BiMoNN), a learnable morphological network with binary inputs and output, inspired by the structure of ConvNets. We replace the convolution by elementary operations from the set of erosions, dilations, anti-erosions, and anti-dilations: we can learn the type of operation and its associated structuring element as well as any intersection/union of these elementary operations.
we show equivalence properties between our neural network and morphological operators. They can be used both as explainable results or as a way to binarize the network: once these equivalences are respected, the morphological operation can replace the neural network. Booleans weights can replace real-valued weights, improving the inference's computing efficiency [1]}, [2]}, [3]}. We demonstrate how we managed to learn some classical morphological operators as well as an intermediate step of a challenging medical imaging problem. A preliminary version of our work is available at [4]}. Our code is publicly available online at https://github.com/TheodoreAouad/Bimonn_DGMM2022.
